标题： 面传递曲面的普查 显示英文标题

标题： A census of face-transitive surfaces

摘要： 一个面传递曲面是一种三角化的二维流形，其自同构群在其三角形集合上作用传递地。 在本文中，我们研究了这一类高度对称的曲面三角化。 我们识别出七种此类面传递曲面，进一步分为总共十三种子类型，这些子类型由它们的自同构群在其上的作用方式区分。 我们利用这些理论结果通过构造立方节点传递图的合适圈双覆盖来计算具有多达1280个面的面传递曲面的普查。 显示英文摘要

摘要： A face-transitive surface is a triangulated 2-dimensional manifold whose automorphism group acts transitively on its set of triangles. In this paper, we investigate this class of highly symmetric surface triangulations. We identify seven types of such face-transitive surfaces, splitting up further into a total of thirteen sub-types, distinguished by how their automorphism groups act on them. We use these theoretical results to compute a census of face-transitive surfaces with up to 1280 faces by constructing suitable cycle double covers of cubic node-transitive graphs.